Options Pricing Calculator
Calculate theoretical option prices and Greeks using Black-Scholes or Binomial Tree pricing.
Option Parameters
Results
Enter parameters and click "Calculate Prices" to see results
Free 160-Page Options Guide
Clear visuals and real examples for every essential concept.
How Option Prices Are Calculated
Option prices are derived from mathematical models that estimate the probability of various stock price outcomes at expiration. The two most common models are Black-Scholes and the Binomial Tree (Cox-Ross-Rubinstein).
Black-Scholes uses a continuous probability distribution and is fast to compute. It's the industry standard for European-style options and works well for American options that won't be exercised early.
Binomial Tree models discrete price movements over multiple time steps. It's more accurate for American options where early exercise might be optimal, such as deep ITM puts or calls approaching an ex-dividend date.
The Greeks
Greeks measure how sensitive an option's price is to changes in underlying factors. Understanding them helps you manage risk and predict how your position will behave.
- Delta (Δ): How much the option price changes per $1 move in the stock. Also approximates the probability of expiring in-the-money.
- Gamma (Γ): How fast delta changes as the stock moves. High gamma means delta shifts rapidly.
- Theta (Θ): How much the option loses per day from time decay, all else equal.
- Vega (ν): How much the option price changes per 1% change in implied volatility.
- Rho (ρ): How much the option price changes per 1% change in interest rates. Usually a minor factor.
Key Inputs
- Stock Price: The current price of the underlying stock.
- Strike Price: The price at which the option can be exercised.
- Days to Expiration: Time remaining until the option expires.
- Implied Volatility: The market's expectation of future price movement. Higher IV means higher option prices.
- Risk-Free Rate: The theoretical return on a risk-free investment (e.g., Treasury bills). Affects option pricing slightly.
- Dividend Yield: The stock's annual dividend as a percentage. Dividends reduce call values and increase put values.
Intrinsic vs Extrinsic Value
An option's price has two components:
- Intrinsic Value: The amount the option is in-the-money. For calls: max(0, stock price − strike). For puts: max(0, strike − stock price).
- Extrinsic Value: Everything above intrinsic value—the "time value" that decays to zero at expiration. This is what theta erodes.
Related Calculators
- Implied Volatility Calculator — Reverse-engineer IV from option prices
- Theta Decay Calculator — Visualize time decay over an option's life
- Long Call Calculator — Visualize call option P/L
- Long Put Calculator — Visualize put option P/L
